Chapter 8

8.7
In Summary
Key Ideas
• When a range of values can vary greatly, using a logarithmic scale with powers
of 10 makes comparisons between the large and small values more manageable.
• Growth and decay situations can be modelled by exponential functions of the
form f(x) 5 ab x . Note that
• f(x) is the final amount or number
• a is the initial amount or number
• for exponential growth, b 5 1 1 growth rate
• for exponential decay, b 5 1 2 decay rate
• x is the number of growth or decay periods
Need to Know
• Scales that measure a wide range of values, such as the pH scale, Richter scale,
and decibel scale, are logarithmic scales.
• To compare concentrations on the pH scale, intensity on the Richter scale, or
sound intensities, determine the quotient between the values being compared.
• Data from a table of values can be graphed and a curve of best fit determined.
If the curve of best fit appears to be exponential, use the regression feature of
the graphing calculator to determine an equation that models the data.
CHECK Your Understanding
1. If one earthquake has a magnitude of 5.2 on the Richter scale and
a second earthquake has a magnitude of 6, compare the intensities
of the two earthquakes.
2. Calculate the pH of a swimming pool with a hydrogen ion
concentration of 6.21 3 10 28 mol>L.
3. A particular sound is 1 000 000 times more intense than a sound you
can just barely hear. What is the loudness of the sound in decibels?
PRACTISING
4. The loudness of a heavy snore is 69 dB. How many times as loud as a
K
normal conversation of 60 dB is a heavy snore?
5. Calculate the hydrogen ion concentration of each substance.
a) baking soda, with a pH of 9
b) milk, with a pH of 6.6
c) an egg, with a pH of 7.8
d) oven cleaner, with a pH of 13
NEL Chapter 8 499